Venn Diagrams I. Venn diagrams

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Presentation transcript:

Venn Diagrams I. Venn diagrams A) Are a way of showing the relationship between sets of events. A specific event is called an element. 1) Shows which set an element is in. 2) Shows if the element is in 2 or more sets at the same time. B) They are normally draw with overlapping circles inside of a rectangular box. This box is called the universe because it contains ALL the elements in the sets. Universe Set A Set B A ∩ B

Venn Diagrams II. Symbols of Venn diagrams A ∩ B Intersection of sets A & B (only want the elements in both A & B) A B A ∪ B Union of sets A & B (we want all the elements in both sets) A B A Δ B Systematic difference between sets (we don't want the elements in both A & B) A B Ac ∩ B = B \ A Relative compliment of A in B (we want everything in B that is not in A) A B Ac = U \ A Absolute compliment of A in U (we want everything in U that is not in A) A B

III. Writing Elements in Venn diagrams A) Write each element in the set that it belongs to (A or B) Write the element in the intersection area if it is a member of both sets. B) If just discussing the number of elements in each set... 1) Write the total number of elements in the universe. 2) Write the number of elements in the intersection of A and B in the A ∩ B area (the overlapping area). 3) Subtract the intersection amount from the Set A total to find how many are in A (but not in A ∩ B) 4) Do the same as # 3 for elements in Set B. Example: 50 members in set A but 15 are in A and B. so set A = 50 – 15 = 35. A ∩ B = 15. Universe Set A Set B A ∩ B

Calc ∩ Stats intersection = 10 students Example: There are 100 seniors at a high school. 60 of them are taking Calculus and 30 are taking STATS. 10 are taking both. A ∩ B = 10 , Set A = 60 – 10 = 50 , set B = 30 – 10 = 20 Calc ∩ Stats intersection = 10 students Calc ∪ Stats union (both sets) = 50 + 10 + 20 = 80 Calc Δ Stats everything in cals & stats but not the intersection 50 + 20 = 70 Stats \ Calc everything in stats but nothing from calc = 20 Calc \ Stats everything in calc but nothing from stats = 50 Seniors \ Calc all the seniors but nothing from calc 100 – ( 50 + 10) = 100 – 60 = 40 Seniors A B 100 Calculus STATS 50 10 20